: Mathematics: supporting hyperplane

mathematical analysis > functional analysis > supporting hyperplane

geometry > convex analysis > convex set > supporting hyperplane

algebra > linear algebra > vector space > topological vector space > supporting hyperplane

supporting hyperplane

In geometry, a supporting hyperplane of a set ${\\displaystyle S}$ $S$ in Euclidean space ${\\displaystyle \\mathbb {R} ^{n}}$ $\\mathbb {R} ^{n}$ is a hyperplane that has both of the following two properties:
- ${\\displaystyle S}$ is entirely contained in one of the two closed half-spaces bounded by the hyperplane,
- ${\\displaystyle S}$ has at least one boundary-point on the hyperplane.

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